pooledVarDP {DPpack}

Differentially Private Pooled Variance

Description

This function computes the differentially private pooled variance from two or more vectors of data at user-specified privacy levels of epsilon and delta.

Usage

pooledVarDP(
  ...,
  eps = 1,
  lower.bound,
  upper.bound,
  which.sensitivity = "bounded",
  mechanism = "Laplace",
  delta = 0,
  type.DP = "aDP",
  approx.n.max = FALSE
)

Arguments

...

Two or more vectors from which to compute the pooled variance.

eps

Positive real number defining the epsilon privacy budget.

lower.bound

Real number giving the global or public lower bound of the input data.

upper.bound

Real number giving the global or public upper bound of the input data.

which.sensitivity

String indicating which type of sensitivity to use. Can be one of 'bounded', 'unbounded', 'both'. If 'bounded' (default), returns result based on bounded definition for differential privacy. If 'unbounded', returns result based on unbounded definition. If 'both', returns result based on both methods (Kifer and Machanavajjhala 2011). Note that if 'both' is chosen, each result individually satisfies (eps, delta)-differential privacy, but may not do so collectively and in composition. Care must be taken not to violate differential privacy in this case.

mechanism

String indicating which mechanism to use for differential privacy. Currently the following mechanisms are supported: 'Laplace', 'Gaussian'. Default is Laplace. See LaplaceMechanism and GaussianMechanism for a description of the supported mechanisms.

delta

Nonnegative real number defining the delta privacy parameter. If 0 (default), reduces to eps-DP and the Laplace mechanism is used.

type.DP

String indicating the type of differential privacy desired for the Gaussian mechanism (if selected). Can be either 'pDP' for probabilistic DP (Machanavajjhala et al. 2008) or 'aDP' for approximate DP (Dwork et al. 2006). Note that if 'aDP' is chosen, epsilon must be strictly less than 1.

approx.n.max

Logical indicating whether to approximate n.max (defined to be the length of the largest input vector) in the computation of the global sensitivity based on the upper and lower bounds of the data (Liu 2019). Approximation is best if n.max is very large.

Value

Sanitized pooled variance based on the bounded and/or unbounded definitions of differential privacy.

References

Dwork C, McSherry F, Nissim K, Smith A (2006). “Calibrating Noise to Sensitivity in Private Data Analysis.” In Halevi S, Rabin T (eds.), Theory of Cryptography, 265–284. ISBN 978-3-540-32732-5, https://doi.org/10.1007/11681878_14.

Kifer D, Machanavajjhala A (2011). “No Free Lunch in Data Privacy.” In Proceedings of the 2011 ACM SIGMOD International Conference on Management of Data, SIGMOD '11, 193–204. ISBN 9781450306614, doi:10.1145/1989323.1989345.

Machanavajjhala A, Kifer D, Abowd J, Gehrke J, Vilhuber L (2008). “Privacy: Theory meets Practice on the Map.” In 2008 IEEE 24th International Conference on Data Engineering, 277-286. doi:10.1109/ICDE.2008.4497436.

Dwork C, Kenthapadi K, McSherry F, Mironov I, Naor M (2006). “Our Data, Ourselves: Privacy Via Distributed Noise Generation.” In Vaudenay S (ed.), Advances in Cryptology - EUROCRYPT 2006, 486–503. ISBN 978-3-540-34547-3, doi:10.1007/11761679_29.

Liu F (2019). “Statistical Properties of Sanitized Results from Differentially Private Laplace Mechanism with Univariate Bounding Constraints.” Transactions on Data Privacy, 12(3), 169-195. http://www.tdp.cat/issues16/tdp.a316a18.pdf.

Examples

# Build datasets
D1 <- stats::rnorm(500, mean=3, sd=2)
D2 <- stats::rnorm(200, mean=3, sd=2)
D3 <- stats::rnorm(100, mean=3, sd=2)
lower.bound <- -3 # 3 standard deviations below mean
upper.bound <- 9 # 3 standard deviations above mean

# Get private pooled variance without approximating n.max
private.pooled.var <- pooledVarDP(D1, D2, D3, eps=1, lower.bound=lower.bound,
                                  upper.bound = upper.bound)
private.pooled.var

# If n.max is sensitive, we can also use
private.pooled.var <- pooledVarDP(D1, D2, D3, eps=1, lower.bound=lower.bound,
                                  upper.bound = upper.bound,
                                  approx.n.max = TRUE)
private.pooled.var